7=2p(2p)-5p+8

Solution for 7=2p(2p)-5p+8 equation:

Simplifying
7 = 2p(2p) + -5p + 8

Remove parenthesis around (2p)
7 = 2p * 2p + -5p + 8

Reorder the terms for easier multiplication:
7 = 2 * 2p * p + -5p + 8

Multiply 2 * 2
7 = 4p * p + -5p + 8

Multiply p * p
7 = 4p2 + -5p + 8

Reorder the terms:
7 = 8 + -5p + 4p2

Solving
7 = 8 + -5p + 4p2

Solving for variable 'p'.

Combine like terms: 7 + -8 = -1
-1 + 5p + -4p2 = 8 + -5p + 4p2 + -8 + 5p + -4p2

Reorder the terms:
-1 + 5p + -4p2 = 8 + -8 + -5p + 5p + 4p2 + -4p2

Combine like terms: 8 + -8 = 0
-1 + 5p + -4p2 = 0 + -5p + 5p + 4p2 + -4p2
-1 + 5p + -4p2 = -5p + 5p + 4p2 + -4p2

Combine like terms: -5p + 5p = 0
-1 + 5p + -4p2 = 0 + 4p2 + -4p2
-1 + 5p + -4p2 = 4p2 + -4p2

Combine like terms: 4p2 + -4p2 = 0
-1 + 5p + -4p2 = 0

Factor a trinomial.
(-1 + p)(1 + -4p) = 0

Subproblem 1
Set the factor '(-1 + p)' equal to zero and attempt to solve:

Simplifying
-1 + p = 0

Solving
-1 + p = 0

Move all terms containing p to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + p = 0 + 1
p = 0 + 1

Combine like terms: 0 + 1 = 1
p = 1

Simplifying
p = 1
Subproblem 2
Set the factor '(1 + -4p)' equal to zero and attempt to solve:

Simplifying
1 + -4p = 0

Solving
1 + -4p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -4p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4p = 0 + -1
-4p = 0 + -1

Combine like terms: 0 + -1 = -1
-4p = -1

Divide each side by '-4'.
p = 0.25

Simplifying
p = 0.25
Solution
p = {1, 0.25}